Uncommon Priors Require Origin Disputes

1. Uncommon Priors Require Origin Disputes Robin Hanson George Mason University ProLogic 2005

2. Clarifying “Objective” Beliefs • Regarding belief as truth estimate • vs. as expression of individuality, or what provokes intellectual progress • Yes, distinguish possible topics of beliefs • what theory to apply now, vs. theory closest to ultimate truth, vs. mix of topics to focus research now • Normative, not positive, claim • Clearly real people with similar info often disagree • But big scientists in big episodes may be wrong • Need not know how to explicitly construct • Constraints: ≥0, Σ=0, update via Bayes’ rule, more? • If enough constraints, result must be unique

3. The Puzzle of Disagreement • Persistent disagreement ubiquitous • Speculative trading, wars, juries, … • Argue in science, politics, family, … • Theory seems to say this irrational • Possible explanations • We’re “just joshing” • Infeasible epistemic rationality • Fixable irrationality: all will change! • Non-epistemic rationality – truth not goal

4. Aumann in 1976 Any information Re possible worlds Common knowledge Of exact E1[x], E2[x] Would say next For Bayesians With common priors If seek truth, not lie Since generalized to Impossible worlds Common Belief A f(•, •), or who max Last ±(E1[x] - E1[E2[x]]) At core, or Wannabe Symmetric prior origins We Can’t Agree to Disagree

5. My Answer: We Self-Deceive • We biased to think better driver, lover, … “I less biased, better data & analysis” • Evolutionary origin: helps us to deceive • Mind “leaks” beliefs via face, voice, … • Leak less if conscious mind really believes • Beliefs like clothes • Function in harsh weather, fashion in mild • When see our self-deception, still disagree • So at some level we accept that we not seek truth

6. Two Faces of Priors • Prior help tell us what to believe • We have beliefs about prior origins/causes • Can this help constrain rational priors?

7. Origins of Priors • Seems irrational to accept some priors • Imagine random brain changes for weird priors • In standard theories, your prior is not special • Species-common DNA • Selected to predict ancestral environment • Individual DNA variations (e.g. personality) • Random by Mendel’s rules of inheritance • Sibling differences independent of everything else! • Culture: random + adapted to local society • But you must think differing prior special! • Can’t express these ideas in standard models

8. Standard Bayesian Model Agent 1 Info Set A Prior Agent 2 Info Set Common Kn. Set

9. An Extended Model Multiple Standard Models With Different Priors

10. Standard Bayesian Model

11. Extending the State Space As event

12. An Extended Model

13. My Differing Prior Was Made Special My prior and any ordinary event E are informative about each other. Given my prior, no other prior is informative about any E, nor is E informative about any other prior.

14. Corollaries My prior only changes if events are more or less likely. If an event is just as likely in situations where my prior is switched with someone else, then those two priors assign the same chance to that event. Only common priors satisfy these and symmetric prior origins.

15. A Tale of Two Astronomers • Disagree if universe open/closed • To justify via priors, must believe: “Nature could not have been just as likely to have switched priors, both if open and if closed” “If I had different prior, would be in situation of different chances” “Given my prior, fact that he has a different prior contains no info” All false if they are brothers!